I'm rather surprised nobody has studied fingernail structure before. Dr. Ennos calls it "ingenious," as the layers of keratin (parallel to the "moon") in the middle layer mean that it has substantial ("almost at tough as horses' hooves") strength along the axis of the finger, but can be easily torn off in strips for reliable trimming.
My own experience in tear-trimming nails is that most of the time (8 times out of 10 or so) the nail tears off more or less cleanly, but the rest of the time the strip widens as it tears, sometimes reaching the nail bed. Not 100% reliable . . .